Soft decision values for Error Control Codes or Error Correction Code (ECC) may be generated based on Log Likelihood Ratios (LLR). When a relatively high-resolution Analog-to-Digital Converter (ADC) is used, the level of a received signal outputted from the relatively high-resolution ADC may be similar to the level of an analog signal actually received. When a metric value is assumed by using a Gaussian Probability Distribution Function (PDF), the metric value may be calculated according to Equation 1:
                                          a            ⁡                          (                              x                ,                y                            )                                =                      log            ⁢                                                  ⁢                          p              ⁡                              (                                  y                  |                  x                                )                                                    ⁢                                  ⁢                                            p              ⁡                              (                                  y                  =                                                                                    y                        n                                            |                      x                                        =                                          x                      m                                                                      )                                      =                                          K                m                            ⁢                              exp                (                                  -                                                                                    (                                                                              y                            n                                                    -                                                      x                            m                                                                          )                                            2                                                              σ                      m                      2                                                                      )                                              ,                                    [                  Equation          ⁢                                          ⁢          1                ]            
where a(x,y) denotes a metric value, x denotes a level of a transmission signal, y denotes an output level of an ADC, yn denotes an n-th output level of an ADC, xm denotes an m-th level of a transmission signal, and Km and σm denote given constants that may be changed depending on m.
Conversely, the difference between the level of a received signal outputted from a relatively low-resolution ADC, and the level of the analog signal actually received, may be increased due to the low-resolution of the ADC.
Because soft decision values calculated according to Equation 1 may be different from actual soft decision values generated based on the LLR when a low-resolution ADC is used, an ECC calculation using the soft decision values may have an error correction capability less than an ECC calculation using the actual soft decision values.